THE AID OF THE ACHROMATIC FRINGES. 25 



fine spectrum fringes will nearly always appear. These are enlarged and 

 centered as specified. A broad slit with the spectroscope removed will then 

 show the achromatic fringes, which may in turn be enlarged and rectified. 

 Horizontal fringes, though often convenient, are at fault, inasmuch as they 

 must rotate with the displacement of the micrometer AN. This appears at 

 once from figure 8, for the center of ellipses is shifted. Vertical fringes alone 

 are free from rotation in relation to AN. 



11. Number of fringes visible, etc. To get the most promising conditions 

 for observing coincidence in case of range finding, the direct and reflected 

 images should be about equally intense. Hence, if a is the coefficient of 

 reflection, the two equal intensities are 



(i a 2 ) = 2(1 a) a 2 , or a= 1/2 



It is best, however, to have a less than this and to darken the direct beam 

 if necessary by a thin half-silver plate interposed in the beam. If a = 1/2 the 

 images are too dark and require higher illumination of the foreground than 

 is usually present. As for the achromatic fringes themselves, they may be 

 obtained with clear plate and opaque mirrors almost as well as with half- 

 silvered plate, if the supernumerary images are partially screened off. With 

 optic plate glass they would not appear. The surprising appearance of 

 satellites i. e., repetitions of the group with increasing faintness is also 

 common with clear plate. 



A series of experiments were made by replacing the half-silver plates with 

 grid-like opaque mirrors. These are easily made by removing the silver along 

 parallel lines (using a T-square) with a sharp wet stick. The slit images 

 were then also gridlike in appearance and the achromatic fringes occurred 

 only on the dark bars. For clearly the superposition of beams takes place 

 on reflection from glass only. In this way the fringes on the supernumerary 

 slit images were identified. These occurred on the bright bars. The two 

 phenomena are therefore complementary. 



The reason for different numbers of visible fringes is less easily understood. 

 In the original experiments two achromatic fringes (black or white) , with about 

 three green-reddish fringes on either side and rapidly fading out, were alone 

 visible. This narrow grid is very advantageous if displacement interfero- 

 metry is in question, for the achromatic fringes are easily recognized. Subse- 

 quently, however, large numbers of less distinctive fringes (20 or more) were 

 usually obtained. As a small number of fringes is as frequently obtained 

 with clear glass as with half-silvered plate, the occurrence is not attributable 

 to the silver. ( 13.) A variety of experiments were made with lenticular 

 compensators, convex or concave, in each beam. The fringes, though 

 obtained without difficulty, were usually rounded and irregular and the 

 results without interest. 



12. Separate adjustable auxiliary mirrors. To obtain strong interfer- 

 ences the two component rays eadT and bfcT of the rectangular inter- 



